import warnings
warnings.filterwarnings("ignore")
import os
import time
import re
import pandas as pd 
import numpy as np
import yellowbrick
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.font_manager import FontProperties
import seaborn as sns
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.cluster import KMeans
from yellowbrick.cluster import KElbowVisualizer
from sklearn import metrics, preprocessing
from sklearn.svm import SVC
from sklearn.metrics import average_precision_score, precision_score, recall_score, f1_score, confusion_matrix, accuracy_score, classification_report, roc_curve, auc, roc_auc_score, silhouette_score
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
from scipy.cluster.hierarchy import linkage, dendrogram, cut_tree
from sklearn import decomposition
import scipy.stats as stats
from scipy.linalg import eigh
from math import factorial as f
from pylab import rcParams
rcParams['figure.figsize'] = 10, 15
%matplotlib inline

vehicle = pd.read_csv("C:/Users/pri96/OneDrive/Documents/AI and ML PGP/Module 5 - Unsupervised Learning (Week 17 to Week 19)/Project/vehicle.csv")
vehicle.head()

print("There are", vehicle.shape[0], "rows and", vehicle.shape[1], "columns in the dataframe")

There are 846 rows and 19 columns in the dataframe

vehicle.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 846 entries, 0 to 845
Data columns (total 19 columns):
 #   Column                       Non-Null Count  Dtype  
---  ------                       --------------  -----  
 0   compactness                  846 non-null    int64  
 1   circularity                  841 non-null    float64
 2   distance_circularity         842 non-null    float64
 3   radius_ratio                 840 non-null    float64
 4   pr.axis_aspect_ratio         844 non-null    float64
 5   max.length_aspect_ratio      846 non-null    int64  
 6   scatter_ratio                845 non-null    float64
 7   elongatedness                845 non-null    float64
 8   pr.axis_rectangularity       843 non-null    float64
 9   max.length_rectangularity    846 non-null    int64  
 10  scaled_variance              843 non-null    float64
 11  scaled_variance.1            844 non-null    float64
 12  scaled_radius_of_gyration    844 non-null    float64
 13  scaled_radius_of_gyration.1  842 non-null    float64
 14  skewness_about               840 non-null    float64
 15  skewness_about.1             845 non-null    float64
 16  skewness_about.2             845 non-null    float64
 17  hollows_ratio                846 non-null    int64  
 18  class                        846 non-null    object 
dtypes: float64(14), int64(4), object(1)
memory usage: 125.7+ KB

# Check percentage of missing values in each column
missing_percentages = vehicle.isnull().mean() * 100

# Print missing percentages
print("Percentage of missing values in each column:")
print(missing_percentages)
vehicle.isnull().sum()

Percentage of missing values in each column:
compactness                    0.000000
circularity                    0.591017
distance_circularity           0.472813
radius_ratio                   0.709220
pr.axis_aspect_ratio           0.236407
max.length_aspect_ratio        0.000000
scatter_ratio                  0.118203
elongatedness                  0.118203
pr.axis_rectangularity         0.354610
max.length_rectangularity      0.000000
scaled_variance                0.354610
scaled_variance.1              0.236407
scaled_radius_of_gyration      0.236407
scaled_radius_of_gyration.1    0.472813
skewness_about                 0.709220
skewness_about.1               0.118203
skewness_about.2               0.118203
hollows_ratio                  0.000000
class                          0.000000
dtype: float64

compactness                    0
circularity                    5
distance_circularity           4
radius_ratio                   6
pr.axis_aspect_ratio           2
max.length_aspect_ratio        0
scatter_ratio                  1
elongatedness                  1
pr.axis_rectangularity         3
max.length_rectangularity      0
scaled_variance                3
scaled_variance.1              2
scaled_radius_of_gyration      2
scaled_radius_of_gyration.1    4
skewness_about                 6
skewness_about.1               1
skewness_about.2               1
hollows_ratio                  0
class                          0
dtype: int64

columns_with_unexpected_values = []
for column in vehicle.columns:
    unique_values = vehicle[column].unique()
    unexpected_values = []
    
    for value in unique_values:
        if pd.isna(value):  # Checking for NaN values
            unexpected_values.append(value)
        elif not pd.api.types.is_numeric_dtype(vehicle[column]) and not isinstance(value, str):
            unexpected_values.append(value)  # Checking for non-string non-numeric values, which is highly unlikely            
    
    if unexpected_values:
        print(f"Column '{column}' has unexpected values: {unexpected_values}")
        columns_with_unexpected_values.append(column)

# Checking for unexpected values across all datapoints (rows)
unexpected_rows = pd.DataFrame(vehicle[vehicle.isnull().any(axis = 1)])
if not unexpected_rows.empty:
    print(f"\nAnd some of those unexpected values across below {len(unexpected_rows)} rows:\n\n")
else:
    print("No unexpected values found across datapoints.")
unexpected_rows.head()

Column 'circularity' has unexpected values: [nan]
Column 'distance_circularity' has unexpected values: [nan]
Column 'radius_ratio' has unexpected values: [nan]
Column 'pr.axis_aspect_ratio' has unexpected values: [nan]
Column 'scatter_ratio' has unexpected values: [nan]
Column 'elongatedness' has unexpected values: [nan]
Column 'pr.axis_rectangularity' has unexpected values: [nan]
Column 'scaled_variance' has unexpected values: [nan]
Column 'scaled_variance.1' has unexpected values: [nan]
Column 'scaled_radius_of_gyration' has unexpected values: [nan]
Column 'scaled_radius_of_gyration.1' has unexpected values: [nan]
Column 'skewness_about' has unexpected values: [nan]
Column 'skewness_about.1' has unexpected values: [nan]
Column 'skewness_about.2' has unexpected values: [nan]

And some of those unexpected values across below 33 rows:

# Imputing above instances of missing values with median
for column in columns_with_unexpected_values:
    vehicle[column].fillna(vehicle.groupby('class')[column].transform('median'),inplace = True)

vehicle.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 846 entries, 0 to 845
Data columns (total 19 columns):
 #   Column                       Non-Null Count  Dtype  
---  ------                       --------------  -----  
 0   compactness                  846 non-null    int64  
 1   circularity                  846 non-null    float64
 2   distance_circularity         846 non-null    float64
 3   radius_ratio                 846 non-null    float64
 4   pr.axis_aspect_ratio         846 non-null    float64
 5   max.length_aspect_ratio      846 non-null    int64  
 6   scatter_ratio                846 non-null    float64
 7   elongatedness                846 non-null    float64
 8   pr.axis_rectangularity       846 non-null    float64
 9   max.length_rectangularity    846 non-null    int64  
 10  scaled_variance              846 non-null    float64
 11  scaled_variance.1            846 non-null    float64
 12  scaled_radius_of_gyration    846 non-null    float64
 13  scaled_radius_of_gyration.1  846 non-null    float64
 14  skewness_about               846 non-null    float64
 15  skewness_about.1             846 non-null    float64
 16  skewness_about.2             846 non-null    float64
 17  hollows_ratio                846 non-null    int64  
 18  class                        846 non-null    object 
dtypes: float64(14), int64(4), object(1)
memory usage: 125.7+ KB

vehicle.describe(include = 'all').T

# Count the occurrences of each class
class_counts = vehicle['class'].value_counts()

# Plotting a pie chart
plt.figure(figsize = (8, 6))
plt.pie(class_counts, labels = class_counts.index, autopct = '%1.1f%%', startangle = 140)
plt.title('Distribution of Classes')
plt.show()

# Print percentage of values for each class
print("Percentage of values for variable 'class':")
print(class_counts / len(vehicle) * 100)

Percentage of values for variable 'class':
class
car    50.709220
bus    25.768322
van    23.522459
Name: count, dtype: float64

duplicate_rows = vehicle[vehicle.duplicated()]

if not duplicate_rows.empty:
    print(f"Number of duplicate rows: {len(duplicate_rows)}")
    print("Duplicate rows:")
    print(duplicate_rows)
else:
    print("No duplicate rows found.")

No duplicate rows found.

sns.pairplot(vehicle, diag_kind = 'kde', hue = 'class')

<seaborn.axisgrid.PairGrid at 0x2e37a01a1d0>

plt.figure(figsize = (15, 8))
sns.heatmap(vehicle.select_dtypes(['float64', 'int64']).corr(), cmap = 'coolwarm', annot = True, fmt = ".2f")

<Axes: >

plt.figure(figsize = (20,15))
sns.boxplot(vehicle, orient = 'h')
plt.title(f"Box Plot for various features combined")
plt.xticks(rotation = 90)
plt.show()

# finding the outliers and replace them by median
outliers = pd.DataFrame()
for col_name in vehicle.columns[:-1]:
    q1 = vehicle[col_name].quantile(0.25)
    q3 = vehicle[col_name].quantile(0.75)
    iqr = q3 - q1
    
    # Defining outlier boundaries
    lower_bound = q1 - 1.5 * iqr
    higher_bound = q3 + 1.5 * iqr
    
    #  Finding rows with outliers
    outlier_rows = vehicle[((vehicle[col_name] < lower_bound) | (vehicle[col_name] > higher_bound))]
    
    # Append to outliers DataFrame
    outliers = pd.concat([outliers, outlier_rows])

print("There are", outliers.shape[0], "rows with outliers which contribute to", 
      format(outliers.shape[0]*100/vehicle.shape[0], '.2f'), "% of overall data. Few  records are - ")
outliers.head()

There are 55 rows with outliers which contribute to 6.50 % of overall data. Few  records are -

# Function to find outliers and replace them with median values grouped by 'class'
def replace_outliers_with_median(vehicle):
    outliers = pd.DataFrame()
    
    # Finding outliers
    for col_name in vehicle.columns[:-1]:  # Excluding the 'class' column
        q1 = vehicle[col_name].quantile(0.25)
        q3 = vehicle[col_name].quantile(0.75)
        iqr = q3 - q1

        # Defining outlier boundaries
        lower_bound = q1 - 1.5 * iqr
        higher_bound = q3 + 1.5 * iqr

        # Finding rows with outliers
        outlier_rows = vehicle[((vehicle[col_name] < lower_bound) | (vehicle[col_name] > higher_bound))]
        
        # Append to outliers DataFrame
        outliers = pd.concat([outliers, outlier_rows])
    print("There are", outliers.shape[0], "rows with outliers which contribute to", 
    format(outliers.shape[0]*100/vehicle.shape[0], '.2f'), "% of overall data")

    # Replace outliers with median values grouped by 'class'
    for col_name in vehicle.columns[:-1]:  # Excluding the 'class' column
        for cls in vehicle['class'].unique():
            # Get the class-specific data
            grouped_by_class = vehicle[vehicle['class'] == cls]
            median_value = grouped_by_class[col_name].median()

            # Replace outliers with the median
            vehicle.loc[outliers[(outliers['class'] == cls) & (outliers[col_name].isin(grouped_by_class[col_name]))].index, col_name] = median_value

    return vehicle

# Example usage:
# Replace outliers in the 'vehicle' DataFrame
vehicle = replace_outliers_with_median(vehicle)

print("Outliers have been replaced with median values grouped by class.")
vehicle.head()

There are 55 rows with outliers which contribute to 6.50 % of overall data
Outliers have been replaced with median values grouped by class.

plt.figure(figsize = (20,15))
sns.boxplot(vehicle, orient = 'h')
plt.title(f"Box Plot for various features combined - After imputing Outliers with medians")
plt.xticks(rotation = 90)
plt.show()

vehicle.describe(include = 'all').T

vehicle['class'].replace(['bus','car','van'],[0,1,2],inplace = True)
vehicle.sample(5, random_state = 42)

# Splitting data into X and Y

X = vehicle.drop('class',axis = 1)  # All independent variables (i.e., excluding 'class' as that is target variable)
y = vehicle['class'] # Target variable

print("Shape of X -->", X.shape)
X.head()

Shape of X --> (846, 18)

print("Shape of y -->", y.shape[0])
y.head()

Shape of y --> 846

0    2
1    2
2    1
3    2
4    0
Name: class, dtype: int64

# Optionally, splitting X and Y into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Shapes of the resulting datasets
print("X_train shape:", X_train.shape)
print("X_test shape:", X_test.shape)
print("Y_train shape:", y_train.shape[0])
print("Y_test shape:", y_test.shape[0])

X_train shape: (676, 18)
X_test shape: (170, 18)
Y_train shape: 676
Y_test shape: 170

# Standardizing the data
standard_scaler = StandardScaler()

# # scaling the training data using the standard scaler and transforming both the training and test data
X_scaled = standard_scaler.fit_transform(X)
X_train_scaled = standard_scaler.fit_transform(X_train)
X_test_scaled = standard_scaler.transform(X_test)

# Converting the scaled data back to DataFrame for better readability
X_scaled_df = pd.DataFrame(X_scaled, columns = X_train.columns)
X_train_scaled_df = pd.DataFrame(X_train_scaled, columns = X_train.columns)
X_test_scaled_df = pd.DataFrame(X_test_scaled, columns = X_test.columns)

# Shapes of the resulting datasets to ensure correctness
print("X_tscaled_df shape:", X_scaled_df.shape)
print("X_train_scaled_df shape:", X_train_scaled_df.shape)
print("X_test_scaled_df shape:", X_test_scaled_df.shape)

print("\nScaled Training Set - ")
X_train_scaled_df.head()

X_tscaled_df shape: (846, 18)
X_train_scaled_df shape: (676, 18)
X_test_scaled_df shape: (170, 18)

Scaled Training Set -

# Create Confusion Matrix
def plot_confusion_matrix(conf_matrix_train, conf_matrix_test):
    fig, axes = plt.subplots(1, 2, figsize=(14, 6))
    sns.heatmap(conf_matrix_train, annot = True, fmt = 'd', cmap = 'Blues', ax = axes[0])
    axes[0].set_title('Confusion Matrix for Training Set')
    axes[0].set_xlabel('Predicted Labels')
    axes[0].set_ylabel('Actual Labels')
    axes[0].set_xticks(ticks = [0.5, 1.5, 2.5], labels = ['bus','car', 'van'])
    axes[0].set_yticks(ticks = [0.5, 1.5, 2.5], labels = ['bus','car', 'van'])

    sns.heatmap(conf_matrix_test, annot = True, fmt = 'd', cmap = 'Blues', ax = axes[1])
    axes[1].set_title('Confusion Matrix for Testing Set')
    axes[1].set_xlabel('Predicted Labels')
    axes[1].set_ylabel('Actual Labels')
    axes[1].set_xticks(ticks = [0.5, 1.5, 2.5], labels = ['bus','car', 'van'])
    axes[1].set_yticks(ticks = [0.5, 1.5, 2.5], labels = ['bus','car', 'van'])
    
    plt.tight_layout()
    plt.show()
    
    print("Confusion Matrix for Final Training Set:\n", conf_matrix_train)
    print("Confusion Matrix for Final Testing Set:\n", conf_matrix_test)

# Create Evaluation Metrics for checking performance of the model
def evaluation_metrics(y_train, y_train_pred, y_test, y_test_pred, conf_matrix_train, conf_matrix_test):
    
    # Compute evaluation metrics for training set
    accuracy_train = accuracy_score(y_train, y_train_pred)
    precision_train = precision_score(y_train, y_train_pred, average='macro')
    recall_train = recall_score(y_train, y_train_pred, average='macro')
    f1_train = f1_score(y_train, y_train_pred, average='macro')
    
    # Compute evaluation metrics for testing set
    accuracy_test = accuracy_score(y_test, y_test_pred)
    precision_test = precision_score(y_test, y_test_pred, average='macro')
    recall_test = recall_score(y_test, y_test_pred, average='macro')
    f1_test = f1_score(y_test, y_test_pred, average='macro')
    
    # Print evaluation metrics on train set
    print("Training Set:")
    print("    Accuracy:", format(accuracy_train, '.3f'))
    print("    Recall:", format(recall_train, '.3f'))
    print("    Precision:", format(precision_train, '.3f'))
    print("    F1 Score:", format(f1_train, '.3f'))
    
    # Print evaluation metrics on test set
    print("Testing Set:")
    print("    Accuracy:", format(accuracy_test, '.3f'))
    print("    Recall:", format(recall_test, '.3f'))
    print("    Precision:", format(precision_test, '.3f'))
    print("    F1 Score:", format(f1_test, '.3f'))
    
    print("\nClassification Report for Training Set:")
    print(classification_report(y_train, y_train_pred))
    
    print("\nClassification Report for Testing Set:")
    print(classification_report(y_test, y_test_pred))
    
    # Plot confusion matrix
    print("\n Confusion Matrix:")
    plot_confusion_matrix(conf_matrix_train, conf_matrix_test)

# Train a base SVM model
svm_model = SVC(random_state = 42)
svm_model

SVC(random_state=42)

SVC(random_state=42)

svm_model.fit(X_train_scaled, y_train)

SVC(random_state=42)

SVC(random_state=42)

# Predicting the train and test set

y_test_pred = svm_model.predict(X_test_scaled)
y_train_pred = svm_model.predict(X_train_scaled)

print("Train Set Accuracy:", format(accuracy_score(y_train, y_train_pred), '.5f'))
print("Test Set Accuracy:", format(accuracy_score(y_test, y_test_pred), '.5f'))

Train Set Accuracy: 0.98669
Test Set Accuracy: 0.97647

# Evaulating the performance of the model on train and test set

conf_matrix_train = confusion_matrix(y_train, y_train_pred)
conf_matrix_test = confusion_matrix(y_test, y_test_pred)

evaluation_metrics(y_train, y_train_pred, y_test, y_test_pred, conf_matrix_train, conf_matrix_test)

Training Set:
    Accuracy: 0.987
    Recall: 0.987
    Precision: 0.985
    F1 Score: 0.986
Testing Set:
    Accuracy: 0.976
    Recall: 0.979
    Precision: 0.972
    F1 Score: 0.975

Classification Report for Training Set:
              precision    recall  f1-score   support

           0       0.99      0.99      0.99       166
           1       0.99      0.99      0.99       351
           2       0.97      0.98      0.98       159

    accuracy                           0.99       676
   macro avg       0.98      0.99      0.99       676
weighted avg       0.99      0.99      0.99       676


Classification Report for Testing Set:
              precision    recall  f1-score   support

           0       1.00      0.96      0.98        52
           1       0.99      0.97      0.98        78
           2       0.93      1.00      0.96        40

    accuracy                           0.98       170
   macro avg       0.97      0.98      0.97       170
weighted avg       0.98      0.98      0.98       170


 Confusion Matrix:

Confusion Matrix for Final Training Set:
 [[165   0   1]
 [  2 346   3]
 [  0   3 156]]
Confusion Matrix for Final Testing Set:
 [[50  1  1]
 [ 0 76  2]
 [ 0  0 40]]

# Creating a table for final comparison of performance
final_comparison = pd.DataFrame({'Model': ['Base Classification SVM Model'],
                                 'Accuracy(Training Set)': format(accuracy_score(y_train, y_train_pred), '.4f'), 
                                 'Accuracy(Testing Set)': format(accuracy_score(y_test, y_test_pred), '.4f')})
final_comparison.style.set_properties(**{'text-align': 'center'}).set_table_styles([{
    'selector': 'th',
    'props': [('text-align', 'center')]
}])

# Initialize PCA with 10 components
pca = PCA(n_components = 10, random_state = 42)
pca

PCA(n_components=10, random_state=42)

PCA(n_components=10, random_state=42)

X_scaled_pca = pca.fit_transform(X_scaled)
X_scaled_pca_df = pd.DataFrame(data = X_scaled_pca, columns=[f'PC{i+1}' for i in range(10)])
X_scaled_pca_df.head()

train_components = pca.fit_transform(X_train_scaled)
train_components_df = pd.DataFrame(data = train_components, columns=[f'PC{i+1}' for i in range(10)])

train_components_df.head()

test_components = pca.transform(X_test_scaled)
test_components_df = pd.DataFrame(data = test_components, columns=[f'PC{i+1}' for i in range(10)])

test_components_df.head()

# Calculating the explained variance ratios
explained_variance_ratio = pca.explained_variance_ratio_
explained_variance_ratio

array([0.54934096, 0.18430257, 0.06879469, 0.06433195, 0.04711015,
       0.0338286 , 0.01812279, 0.01267838, 0.00618011, 0.00415381])

cumulative_explained_variance = explained_variance_ratio.cumsum()
cumulative_explained_variance

array([0.54934096, 0.73364353, 0.80243822, 0.86677017, 0.91388031,
       0.94770891, 0.9658317 , 0.97851008, 0.98469019, 0.988844  ])

# Printing explained variance ratios for each principal component
print("Explained Variance Ratios:")
for i, evr in enumerate(explained_variance_ratio):
    print(f"    PC{i+1}: {evr:.5f}")

Explained Variance Ratios:
    PC1: 0.54934
    PC2: 0.18430
    PC3: 0.06879
    PC4: 0.06433
    PC5: 0.04711
    PC6: 0.03383
    PC7: 0.01812
    PC8: 0.01268
    PC9: 0.00618
    PC10: 0.00415

# Printing explained variance ratios for each principal component
print("Cumulative Variance:")
for i, cumulative_var in enumerate(cumulative_explained_variance, 1):
    print(f"    Component {i}: {cumulative_var:.5f}")

Cumulative Variance:
    Component 1: 0.54934
    Component 2: 0.73364
    Component 3: 0.80244
    Component 4: 0.86677
    Component 5: 0.91388
    Component 6: 0.94771
    Component 7: 0.96583
    Component 8: 0.97851
    Component 9: 0.98469
    Component 10: 0.98884

overall_variance_explained = np.sum(explained_variance_ratio)
print(f"Overall Variance Explained by 10 PCA components: {overall_variance_explained:.4f}")

Overall Variance Explained by 10 PCA components: 0.9888

# Visualization of above
plt.figure(figsize = (10, 6))
plt.plot(range(1, len(cumulative_explained_variance) + 1), cumulative_explained_variance, marker = 'o',
         linestyle = '--', color = 'b')
plt.title('Cumulative Variance Explained by Number of Principal Components (Total = 10)')
plt.xlabel('Number of Principal Components')
plt.ylabel('Cumulative Explained Variance')
plt.grid(True)
plt.show()

# Adding a horizontal line to highlight the threshold of 90%
plt.figure(figsize = (10, 6))
plt.plot(range(1, len(cumulative_explained_variance) + 1), cumulative_explained_variance, marker = 'o',
         linestyle = '--', color = 'b')
plt.axhline(y = 0.90, color = 'r', linestyle = '-')
plt.title('Cumulative Variance Explained by Number of Principal Components (Total = 10)')
plt.xlabel('Number of Principal Components')
plt.ylabel('Cumulative Explained Variance')
plt.xticks(range(1, len(cumulative_explained_variance) + 1))
plt.grid(True)
plt.show()

# Determine the number of components for 90% variance
num_components = np.argmax(cumulative_explained_variance >= 0.90) + 1
print(" The suitable number of minimum compoenents to explain 90% or more variance is -", num_components)

 The suitable number of minimum compoenents to explain 90% or more variance is - 5

pca_90 = PCA(n_components = num_components, random_state = 42)
pca_90

PCA(n_components=5, random_state=42)

PCA(n_components=5, random_state=42)

X_scaled_pca_90 = pca_90.fit_transform(X_scaled)
X_scaled_pca_90_df = pd.DataFrame(data = X_scaled_pca_90, columns=[f'PC_90_{i+1}' for i in range(num_components)])

print("There are", X_scaled_pca_90_df.shape[0], "rows and", X_scaled_pca_90_df.shape[1], "columns in the below dataframe")
X_scaled_pca_90_df.head()

There are 846 rows and 5 columns in the below dataframe

train_components_90 = pca_90.fit_transform(X_train_scaled)
train_components_90_df = pd.DataFrame(data = train_components_90, columns=[f'PC_90_{i+1}' for i in range(num_components)])

print("There are", train_components_90_df.shape[0], "rows and", train_components_90_df.shape[1], "columns in the below dataframe")
train_components_90_df.head()

There are 676 rows and 5 columns in the below dataframe

test_components_90 = pca_90.transform(X_test_scaled)
test_components_90_df = pd.DataFrame(data = test_components_90, columns=[f'PC_90_{i+1}' for i in range(num_components)])

print("There are", test_components_90_df.shape[0], "rows and", test_components_90_df.shape[1], "columns in the below dataframe")
test_components_90_df.head()

There are 170 rows and 5 columns in the below dataframe

explained_variance_ratio_90 = pca_90.explained_variance_ratio_
cumulative_explained_variance_90 = explained_variance_ratio_90.cumsum()

# Adding a horizontal line to highlight the threshold of 90%
plt.figure(figsize = (10, 6))
plt.plot(range(1, len(cumulative_explained_variance_90) + 1), cumulative_explained_variance_90, marker = 'o',
         linestyle = '--', color = 'b')
plt.axhline(y = 0.90, color = 'r', linestyle = '-')
plt.title('Cumulative Variance Explained by Number of Principal Components (Total = 5)')
plt.xlabel('Number of Principal Components')
plt.ylabel('Cumulative Explained Variance')
plt.xticks(range(1, len(cumulative_explained_variance_90) + 1))
plt.grid(True)
plt.show()

overall_variance_explained_90 = np.sum(explained_variance_ratio_90)
print(f"Overall Variance Explained by minimum number of PCA components : {overall_variance_explained_90:.4f}")

Overall Variance Explained by minimum number of PCA components : 0.9139

# Initializing the SVM classifier
svm_pca_90 = SVC(random_state = 42)
svm_pca_90

SVC(random_state=42)

SVC(random_state=42)

# Training SVM on the PCA-transformed training data
svm_pca_90.fit(train_components_90_df, y_train)

SVC(random_state=42)

SVC(random_state=42)

# Predicting the train and test set

y_test_pca_90_pred = svm_pca_90.predict(test_components_90)
y_train_pca_90_pred = svm_pca_90.predict(train_components_90)

print("Train Set Accuracy:", format(accuracy_score(y_train, y_train_pca_90_pred), '.5f'))
print("Test Set Accuracy:", format(accuracy_score(y_test, y_test_pca_90_pred), '.5f'))

Train Set Accuracy: 0.91272
Test Set Accuracy: 0.89412

# Evaulating the performance of the model on train and test set

conf_matrix_train = confusion_matrix(y_train, y_train_pca_90_pred)
conf_matrix_test = confusion_matrix(y_test, y_test_pca_90_pred)

evaluation_metrics(y_train, y_train_pca_90_pred, y_test, y_test_pca_90_pred, conf_matrix_train, conf_matrix_test)

Training Set:
    Accuracy: 0.913
    Recall: 0.909
    Precision: 0.907
    F1 Score: 0.908
Testing Set:
    Accuracy: 0.894
    Recall: 0.896
    Precision: 0.887
    F1 Score: 0.890

Classification Report for Training Set:
              precision    recall  f1-score   support

           0       0.93      0.95      0.94       166
           1       0.93      0.92      0.92       351
           2       0.87      0.86      0.86       159

    accuracy                           0.91       676
   macro avg       0.91      0.91      0.91       676
weighted avg       0.91      0.91      0.91       676


Classification Report for Testing Set:
              precision    recall  f1-score   support

           0       0.94      0.90      0.92        52
           1       0.92      0.88      0.90        78
           2       0.80      0.90      0.85        40

    accuracy                           0.89       170
   macro avg       0.89      0.90      0.89       170
weighted avg       0.90      0.89      0.90       170


 Confusion Matrix:

Confusion Matrix for Final Training Set:
 [[158   7   1]
 [  8 323  20]
 [  4  19 136]]
Confusion Matrix for Final Testing Set:
 [[47  4  1]
 [ 1 69  8]
 [ 2  2 36]]

# Adding values in comparison table table for final comparison of performance
temp_dataframe = pd.DataFrame({'Model': ['SVM Model (PCA with 5 components)'],
                                 'Accuracy(Training Set)': format(accuracy_score(y_train, y_train_pca_90_pred), '.4f'), 
                                 'Accuracy(Testing Set)': format(accuracy_score(y_test, y_test_pca_90_pred), '.4f')})

final_comparison = pd.concat([final_comparison, temp_dataframe])
final_comparison

# printing the X_scaled_pca_90 dataframe
X_scaled_pca_90_df.head()

# Let's perform train-test split on this PCA-transformed data
X_scaled_pca_90_train, X_scaled_pca_90_test, y_train, y_test = train_test_split(X_scaled_pca_90,
                                                                                y, test_size = 0.2, random_state = 42)

# Shapes of the resulting datasets
print("X_scaled_pca_90_test shape:", X_scaled_pca_90_train.shape)
print("X_scaled_pca_90_test shape:", X_scaled_pca_90_test.shape)
print("Y_train shape:", y_train.shape[0])
print("Y_test shape:", y_test.shape[0])

X_scaled_pca_90_test shape: (676, 5)
X_scaled_pca_90_test shape: (170, 5)
Y_train shape: 676
Y_test shape: 170

# Now, let's initialize our new SVM model
svm_tuned = SVC(random_state = 42)
svm_tuned

SVC(random_state=42)

SVC(random_state=42)

# Defining parameter grid for GridSearchCV
param_grid = {
    'C': [0.1, 1, 10, 100],
    'gamma': [0.1, 1, 10, 100],
    'kernel': ['linear', 'rbf']#, 'poly'],
    #'degree': [2, 3, 4]
}

# Initializing GridSearchCV
grid_search = GridSearchCV(estimator = svm_tuned, param_grid = param_grid,
                           cv = 5, scoring = 'accuracy', verbose = 1, n_jobs = -1)

grid_search

GridSearchCV(cv=5, estimator=SVC(random_state=42), n_jobs=-1,
             param_grid={'C': [0.1, 1, 10, 100], 'gamma': [0.1, 1, 10, 100],
                         'kernel': ['linear', 'rbf']},
             scoring='accuracy', verbose=1)

GridSearchCV(cv=5, estimator=SVC(random_state=42), n_jobs=-1,
             param_grid={'C': [0.1, 1, 10, 100], 'gamma': [0.1, 1, 10, 100],
                         'kernel': ['linear', 'rbf']},
             scoring='accuracy', verbose=1)

SVC(random_state=42)

SVC(random_state=42)

# Performing Grid Search to find best parameters

start_time_fit = time.time();
fit_grid_search = grid_search.fit(X_scaled_pca_90_train, y_train)
end_time_fit = time.time();

print("SVM Grid Search Tuning on PCA-transformed data Time:", 
      format((end_time_fit - start_time_fit), '.2f'), "seconds")

print("\n Fitted Model - \n")
fit_grid_search
fit_grid_search

Fitting 5 folds for each of 32 candidates, totalling 160 fits
SVM Grid Search Tuning on PCA-transformed data Time: 3.93 seconds

 Fitted Model -

GridSearchCV(cv=5, estimator=SVC(random_state=42), n_jobs=-1,
             param_grid={'C': [0.1, 1, 10, 100], 'gamma': [0.1, 1, 10, 100],
                         'kernel': ['linear', 'rbf']},
             scoring='accuracy', verbose=1)

GridSearchCV(cv=5, estimator=SVC(random_state=42), n_jobs=-1,
             param_grid={'C': [0.1, 1, 10, 100], 'gamma': [0.1, 1, 10, 100],
                         'kernel': ['linear', 'rbf']},
             scoring='accuracy', verbose=1)

SVC(random_state=42)

SVC(random_state=42)

# Getting the best parameters found by Grid Search
best_parameters = grid_search.best_params_
print("Best Parameters found by Grid Search on PCA-transformed data - \n       ", best_parameters)

Best Parameters found by Grid Search on PCA-transformed data - 
        {'C': 10, 'gamma': 0.1, 'kernel': 'rbf'}

best_model = grid_search.best_estimator_
best_model.fit(X_scaled_pca_90_train, y_train)

SVC(C=10, gamma=0.1, random_state=42)

SVC(C=10, gamma=0.1, random_state=42)

y_train_pred_tuned = best_model.predict(X_scaled_pca_90_train)
y_test_pred_tuned = best_model.predict(X_scaled_pca_90_test)

print("Train Set Accuracy:", format(accuracy_score(y_train, y_train_pred_tuned), '.5f'))
print("Test Set Accuracy:", format(accuracy_score(y_test, y_test_pred_tuned), '.5f'))

Train Set Accuracy: 0.95266
Test Set Accuracy: 0.90588

# Evaulating the performance of the model on train and test set

conf_matrix_train = confusion_matrix(y_train, y_train_pred_tuned)
conf_matrix_test = confusion_matrix(y_test, y_test_pred_tuned)

evaluation_metrics(y_train, y_train_pred_tuned, y_test, y_test_pred_tuned, conf_matrix_train, conf_matrix_test)

Training Set:
    Accuracy: 0.953
    Recall: 0.950
    Precision: 0.950
    F1 Score: 0.950
Testing Set:
    Accuracy: 0.906
    Recall: 0.903
    Precision: 0.901
    F1 Score: 0.902

Classification Report for Training Set:
              precision    recall  f1-score   support

           0       0.96      0.98      0.97       166
           1       0.96      0.96      0.96       351
           2       0.93      0.92      0.92       159

    accuracy                           0.95       676
   macro avg       0.95      0.95      0.95       676
weighted avg       0.95      0.95      0.95       676


Classification Report for Testing Set:
              precision    recall  f1-score   support

           0       0.96      0.92      0.94        52
           1       0.91      0.91      0.91        78
           2       0.83      0.88      0.85        40

    accuracy                           0.91       170
   macro avg       0.90      0.90      0.90       170
weighted avg       0.91      0.91      0.91       170


 Confusion Matrix:

Confusion Matrix for Final Training Set:
 [[162   3   1]
 [  5 336  10]
 [  1  12 146]]
Confusion Matrix for Final Testing Set:
 [[48  3  1]
 [ 1 71  6]
 [ 1  4 35]]

# Adding values in comparison table table for final comparison of performance
temp_dataframe = pd.DataFrame({'Model': ['SVM Model Tuned (PCA-transformed)'],
                                 'Accuracy(Training Set)': format(accuracy_score(y_train, y_train_pred_tuned), '.4f'), 
                                 'Accuracy(Testing Set)': format(accuracy_score(y_test, y_test_pred_tuned), '.4f')})

final_comparison = pd.concat([final_comparison, temp_dataframe])

final_comparison

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
0	95	48.0	83.0	178.0	72.0	10	162.0	42.0	20.0	159	176.0	379.0	184.0	70.0	6.0	16.0	187.0	197	van
1	91	41.0	84.0	141.0	57.0	9	149.0	45.0	19.0	143	170.0	330.0	158.0	72.0	9.0	14.0	189.0	199	van
2	104	50.0	106.0	209.0	66.0	10	207.0	32.0	23.0	158	223.0	635.0	220.0	73.0	14.0	9.0	188.0	196	car
3	93	41.0	82.0	159.0	63.0	9	144.0	46.0	19.0	143	160.0	309.0	127.0	63.0	6.0	10.0	199.0	207	van
4	85	44.0	70.0	205.0	103.0	52	149.0	45.0	19.0	144	241.0	325.0	188.0	127.0	9.0	11.0	180.0	183	bus

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
5	107	NaN	106.0	172.0	50.0	6	255.0	26.0	28.0	169	280.0	957.0	264.0	85.0	5.0	9.0	181.0	183	bus
9	93	44.0	98.0	NaN	62.0	11	183.0	36.0	22.0	146	202.0	505.0	152.0	64.0	4.0	14.0	195.0	204	car
19	101	56.0	100.0	215.0	NaN	10	208.0	32.0	24.0	169	227.0	651.0	223.0	74.0	6.0	5.0	186.0	193	car
35	100	46.0	NaN	172.0	67.0	9	157.0	43.0	20.0	150	170.0	363.0	184.0	67.0	17.0	7.0	192.0	200	van
66	81	43.0	68.0	125.0	57.0	8	149.0	46.0	19.0	146	169.0	323.0	172.0	NaN	NaN	18.0	179.0	184	bus

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
compactness	846.0	NaN	NaN	NaN	93.678487	8.234474	73.0	87.0	93.0	100.0	119.0
circularity	846.0	NaN	NaN	NaN	44.826241	6.13434	33.0	40.0	44.0	49.0	59.0
distance_circularity	846.0	NaN	NaN	NaN	82.066194	15.754263	40.0	70.0	80.0	98.0	112.0
radius_ratio	846.0	NaN	NaN	NaN	168.916076	33.427561	104.0	141.0	167.25	195.0	333.0
pr.axis_aspect_ratio	846.0	NaN	NaN	NaN	61.680851	7.882557	47.0	57.0	61.0	65.0	138.0
max.length_aspect_ratio	846.0	NaN	NaN	NaN	8.567376	4.601217	2.0	7.0	8.0	10.0	55.0
scatter_ratio	846.0	NaN	NaN	NaN	168.920804	33.199802	112.0	147.0	157.0	198.0	265.0
elongatedness	846.0	NaN	NaN	NaN	40.927896	7.813401	26.0	33.0	43.0	46.0	61.0
pr.axis_rectangularity	846.0	NaN	NaN	NaN	20.579196	2.590879	17.0	19.0	20.0	23.0	29.0
max.length_rectangularity	846.0	NaN	NaN	NaN	147.998818	14.515652	118.0	137.0	146.0	159.0	188.0
scaled_variance	846.0	NaN	NaN	NaN	188.643026	31.37802	130.0	167.0	179.0	217.0	320.0
scaled_variance.1	846.0	NaN	NaN	NaN	439.665485	176.492876	184.0	318.25	364.0	586.75	1018.0
scaled_radius_of_gyration	846.0	NaN	NaN	NaN	174.712766	32.546284	109.0	149.0	174.0	198.0	268.0
scaled_radius_of_gyration.1	846.0	NaN	NaN	NaN	72.443262	7.470873	59.0	67.0	71.0	75.0	135.0
skewness_about	846.0	NaN	NaN	NaN	6.356974	4.904073	0.0	2.0	6.0	9.0	22.0
skewness_about.1	846.0	NaN	NaN	NaN	12.604019	8.930921	0.0	5.0	11.0	19.0	41.0
skewness_about.2	846.0	NaN	NaN	NaN	188.919622	6.152167	176.0	184.0	188.0	193.0	206.0
hollows_ratio	846.0	NaN	NaN	NaN	195.632388	7.438797	181.0	190.25	197.0	201.0	211.0
class	846	3	car	429	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
37	90	48.0	86.0	306.0	126.0	49	153.0	44.0	19.0	156	272.0	346.0	200.0	118.0	0.0	15.0	185.0	194	van
135	89	47.0	83.0	322.0	133.0	48	158.0	43.0	20.0	163	229.0	364.0	176.0	97.0	0.0	14.0	184.0	194	van
388	94	47.0	85.0	333.0	138.0	49	155.0	43.0	19.0	155	320.0	354.0	187.0	135.0	12.0	9.0	188.0	196	van
4	85	44.0	70.0	205.0	103.0	52	149.0	45.0	19.0	144	241.0	325.0	188.0	127.0	9.0	11.0	180.0	183	bus
37	90	48.0	86.0	306.0	126.0	49	153.0	44.0	19.0	156	272.0	346.0	200.0	118.0	0.0	15.0	185.0	194	van

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
0	95	48.0	83.0	178.0	72.0	10	162.0	42.0	20.0	159	176.0	379.0	184.0	70.0	6.0	16.0	187.0	197	van
1	91	41.0	84.0	141.0	57.0	9	149.0	45.0	19.0	143	170.0	330.0	158.0	72.0	9.0	14.0	189.0	199	van
2	104	50.0	106.0	209.0	66.0	10	207.0	32.0	23.0	158	223.0	635.0	220.0	73.0	14.0	9.0	188.0	196	car
3	93	41.0	82.0	159.0	63.0	9	144.0	46.0	19.0	143	160.0	309.0	127.0	63.0	6.0	10.0	199.0	207	van
4	89	44.0	72.0	167.5	64.0	6	152.0	44.0	19.0	145	177.0	344.0	176.0	76.0	5.0	10.0	186.0	189	bus

ONLY HERE FOR SCENARIO WITH OUTLER DETECTION AND IMPUTATION SCENARIO.
THIS IS NOT THE ACTUAL PROJECT. PLEASE REFER OTHER FILE FOR "PART A" AND FULL PROJECT

PART B¶

QUESTION 1¶

SOLUTION (1 A.)¶

SOLUTION (1 B.)¶

SOLUTION (1 C.)¶

SOLUTION (1 D.)¶

PAIR PLOT¶

CORRELATION & HEAT MAP¶

BOX PLOT¶

QUESTION 2¶

SOLUTION (2 A.)¶

SOLUTION (2 B.)¶

QUESTION 3¶

SOLUTION (3 A.)¶

SOLUTION (3 B.)¶

SOLUTION (3 C.)¶

SOLUTION (3 D.)¶

SOLUTION (3 E.)¶

SOLUTION (3 F.)¶

SOLUTION (3 G.)¶

SOLUTION (3 H.)¶

QUESTION 4¶

SOLUTION (4 A.)¶

SOLUTION (4 B.)¶

SOLUTION (4 C.)¶

QUESTION 5¶

SOLUTION (5 A.)¶

SOLUTION (5 B.)¶

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
compactness	846.0	NaN	NaN	NaN	93.567376	7.937452	73.0	88.0	93.0	99.0	116.0
circularity	846.0	NaN	NaN	NaN	44.776596	6.000471	33.0	40.0	44.0	49.0	59.0
distance_circularity	846.0	NaN	NaN	NaN	82.098109	15.376184	40.0	70.0	79.0	96.0	112.0
radius_ratio	846.0	NaN	NaN	NaN	167.925532	31.150509	104.0	142.0	167.5	193.0	246.0
pr.axis_aspect_ratio	846.0	NaN	NaN	NaN	61.190307	5.530374	47.0	57.0	61.0	65.0	76.0
max.length_aspect_ratio	846.0	NaN	NaN	NaN	8.120567	2.026365	3.0	7.0	8.0	10.0	13.0
scatter_ratio	846.0	NaN	NaN	NaN	168.6513	32.383284	112.0	146.0	157.0	196.75	262.0
elongatedness	846.0	NaN	NaN	NaN	40.917258	7.635344	26.0	33.25	43.0	46.0	61.0
pr.axis_rectangularity	846.0	NaN	NaN	NaN	20.549645	2.532958	17.0	19.0	20.0	23.0	28.0
max.length_rectangularity	846.0	NaN	NaN	NaN	147.916076	14.2083	118.0	137.0	146.0	158.75	188.0
scaled_variance	846.0	NaN	NaN	NaN	187.841608	29.941339	130.0	167.0	178.0	214.0	288.0
scaled_variance.1	846.0	NaN	NaN	NaN	437.725768	171.764061	184.0	318.0	364.5	576.0	987.0
scaled_radius_of_gyration	846.0	NaN	NaN	NaN	174.334515	31.80001	109.0	150.0	174.0	196.75	268.0
scaled_radius_of_gyration.1	846.0	NaN	NaN	NaN	72.021277	6.094873	59.0	68.0	71.0	75.0	87.0
skewness_about	846.0	NaN	NaN	NaN	6.153664	4.545109	0.0	2.0	6.0	9.0	19.0
skewness_about.1	846.0	NaN	NaN	NaN	12.567376	8.761107	0.0	6.0	11.0	18.0	40.0
skewness_about.2	846.0	NaN	NaN	NaN	188.938534	6.001657	176.0	185.0	188.0	193.0	204.0
hollows_ratio	846.0	NaN	NaN	NaN	195.661939	7.243468	181.0	191.0	197.0	201.0	211.0
class	846	3	car	429	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio
0	-0.447383	0.367465	0.185274	-0.237831	0.487192	0.904825	-0.167288	0.135616	-0.205454	0.844217	-0.351616	-0.276018	0.355914	0.198339	0.621442	-1.460108	-0.668052	-0.135318
1	1.069828	1.194934	1.239419	1.422429	0.487192	0.904825	1.098723	-1.060166	1.012853	0.635555	0.920385	1.085722	0.387751	-1.132454	-1.360137	0.703190	0.644271	0.980233
2	1.449131	1.360428	1.700607	1.198933	0.305436	1.896174	1.700079	-1.325895	1.825058	1.400648	1.332926	1.661612	0.865317	-0.134359	1.942494	2.524914	-0.011891	0.980233
3	2.713474	1.194934	1.173535	1.103148	0.123680	0.904825	1.541827	-1.325895	1.418956	1.191986	1.436061	1.571629	1.279207	0.031990	1.722319	-1.004677	-0.175931	0.143570
4	1.954868	1.691415	0.909999	0.720011	-0.785100	-1.077871	2.301434	-1.724490	2.231161	1.539756	2.742440	2.531446	2.170663	2.194529	0.401266	-0.435388	-0.832093	-1.669202

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10
0	0.616786	-0.656198	-0.588809	0.675499	-0.834970	-1.875319	-0.159352	0.681260	0.300094	0.182714
1	-1.528457	-0.350607	-0.247520	-1.333410	-0.241597	-0.106052	0.207227	-0.123113	-0.162492	-0.357933
2	4.036602	0.253970	-1.251445	-0.166392	0.964006	-0.634244	0.846855	-0.145021	0.328844	-0.499040
3	-1.546115	-3.101297	-0.475628	-0.411329	-0.616389	0.373662	0.114184	0.189917	-0.351054	0.293456
4	-1.495061	0.933869	-0.118030	1.152771	0.392378	-0.422421	-0.296414	0.101058	0.264962	0.103133

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10
0	0.078779	0.724597	1.881145	0.334867	-0.782546	-0.696754	0.367182	-0.190328	-0.169587	0.151643
1	3.661733	-1.306332	-1.137874	0.286916	-1.076376	0.207300	-0.244219	0.063574	0.290371	0.247014
2	5.349105	-0.343910	-0.481351	-2.351430	0.993502	-1.577530	0.086273	0.253858	-0.372301	0.107853
3	4.830518	0.559451	1.611400	-0.468141	0.952707	0.788349	0.944737	0.886320	0.408963	-0.115990
4	5.341616	3.967103	-0.357915	0.545154	1.949493	1.920468	-0.164908	0.440096	-0.211912	-0.156900

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10
0	-1.664303	1.004923	1.184971	2.663422	0.556912	-1.293941	-0.005094	-0.611842	0.076082	0.451762
1	-3.593773	1.739502	0.885594	-1.433330	0.396088	0.438236	0.930078	0.999913	0.301610	0.011017
2	-2.562531	2.743790	-1.087999	0.060070	-0.528041	0.301019	-0.274937	0.596780	0.117052	-0.304579
3	-2.023648	0.706398	1.194657	-0.575487	2.059044	-0.865997	0.286400	-0.386585	0.546185	0.209683
4	-2.093355	2.919766	-0.363971	0.082303	-0.429702	-0.371410	-0.884668	-0.519972	-0.192239	-0.178418

	Model	Accuracy(Training Set)	Accuracy(Testing Set)
0	Base Classification SVM Model	0.9867	0.9765
0	SVM Model (PCA with 5 components)	0.9127	0.8941

ONLY HERE FOR SCENARIO WITH OUTLER DETECTION AND IMPUTATION SCENARIO. THIS IS NOT THE ACTUAL PROJECT. PLEASE REFER OTHER FILE FOR "PART A" AND FULL PROJECT

PART B¶

QUESTION 1¶

*SOLUTION (1 A.)*¶

*SOLUTION (1 B.)*¶

*SOLUTION (1 C.)*¶

*SOLUTION (1 D.)*¶

PAIR PLOT¶

CORRELATION & HEAT MAP¶

BOX PLOT¶

QUESTION 2¶

*SOLUTION (2 A.)*¶

*SOLUTION (2 B.)*¶

QUESTION 3¶

*SOLUTION (3 A.)*¶

*SOLUTION (3 B.)*¶

*SOLUTION (3 C.)*¶

*SOLUTION (3 D.)*¶

*SOLUTION (3 E.)*¶

*SOLUTION (3 F.)*¶

*SOLUTION (3 G.)*¶

*SOLUTION (3 H.)*¶

QUESTION 4¶

*SOLUTION (4 A.)*¶

*SOLUTION (4 B.)*¶

*SOLUTION (4 C.)*¶

QUESTION 5¶

*SOLUTION (5 A.)*¶

*SOLUTION (5 B.)*¶

ONLY HERE FOR SCENARIO WITH OUTLER DETECTION AND IMPUTATION SCENARIO.
THIS IS NOT THE ACTUAL PROJECT. PLEASE REFER OTHER FILE FOR "PART A" AND FULL PROJECT

SOLUTION (1 A.)¶

SOLUTION (1 B.)¶

SOLUTION (1 C.)¶

SOLUTION (1 D.)¶

SOLUTION (2 A.)¶

SOLUTION (2 B.)¶

SOLUTION (3 A.)¶

SOLUTION (3 B.)¶

SOLUTION (3 C.)¶

SOLUTION (3 D.)¶

SOLUTION (3 E.)¶

SOLUTION (3 F.)¶

SOLUTION (3 G.)¶

SOLUTION (3 H.)¶

SOLUTION (4 A.)¶

SOLUTION (4 B.)¶

SOLUTION (4 C.)¶

SOLUTION (5 A.)¶

SOLUTION (5 B.)¶